Can't remember an old PS2 game?

When i was younger, i had a PS2 i believe, and only two games. One was a nascar type game, the other was a game where I played a green lizard/gecko and collected bananas. At the stage selection screen, you could fall off and die, which would change the world you entered (entering the world consisted of going through giant portal with a faint outline of the world) In the game, there were giant venus fly traps that would try to eat you, and to defeat them I think you had to dodge them when they lunged for you, then hit them while they were stuck. Another part of the game is where you could go down a rabbit hole, and suddenly gain Bugs Bunny ears, and Elmer Fudd tries to shoot you. Past where Elmer walks around, there is a waterfall that you could climb up to advance in the level, but it was almost impossible to climb. I can not remember the name of the game for the life of me,someone please help!!!